Retarder stacks for polarizing a first color spectrum along a first axis and a second color spectrum along a second axis

ABSTRACT

This invention provides a complementary color polarizer using a single polarizing film followed by a stack of two or more retarders. In a preferred embodiment, the color polarizers of this invention produce orthogonally polarized complementary primary colors (red/cyan, green/magenta, or blue/yellow). This invention further provides color filters which utilize the color polarizers of this invention in combination with a polarization separator to separate the orthogonally polarized colors. The polarization separator can be passive, such as a polarizing beam splitter, or active, such as a switchable polarizer. The switchable polarizer can employ a nematic or a smectic liquid crystal cell. Two color filters of this invention can be cascaded to provide a three color (RGB) filter with an off-state. In combination with a monochrome display or camera, the color filters of this invention provide color displays or cameras.

This application is a continuation of U.S. application Ser. No.08/447,522 filed May 23, 1995 now U.S. Pat. No. 5,751,384.

FIELD OF THE INVENTION

This invention pertains to color polarizers consisting of a polarizer incombination with a stack of retardation films, and to their use inliquid crystal switchable color filters and color displays with highsaturation and high throughput.

BACKGROUND OF THE INVENTION Switched Polarizer Filters

There are two basic classes of liquid crystal color switching filters:polarization interference filters (PIFs) and switched-polarizer-filters(SPFs). The basic unit of an SPF is a stage, consisting of a colorpolarizer and a two-state neutral polarization switch. This class isintrinsically binary tunable, such that each filter stage permitsswitching between two colors. Stages are cascaded in order to provideadditional output colors. Color polarizers used in SPFs include singleretardation films on neutral linear polarizers and pleochroic colorpolarizing filters. The polarization switch can be a liquid crystal (LC)polarization switch preceding a static polarization analyzer. The switchoptimally provides neutral polarization switching. The chromatic natureof the active element degrades performance and is ideally suppressed inan SPF.

Shutters based on a color polarizer consisting of a neutral-polarizerfollowed by a single retarder are well reported in the art (for examplein U.S. Pat. No. 4,003,081 to Hilsum, U.S. Pat. No. 4,091,808 toScheffer and U.S. Pat. No. 4,232,984 to Shanks). While thepolarizer/retarder structure can be described as a complementary colorpolarizer in the sense that it is possible to produce two distinct huesby rotating the polarizer through 90 degrees, using this type of colorpolarizer in an SPF does not result in saturated colors.

Shutters based on pleochroic color polarizers are also well reported(for example in U.S. Pat. No. 4,582,396 to Bos, U.S. Pat. No. 4,416,514to Plummer, U.S. Pat. No. 4,758,818 to Vatne and U.S. Pat. No. 5,347,378to Handschy). Pleochroic color polarizers are films that function aslinear polarizers in specific wavelength bands. They are formed bydoping a polymer with long-chain pleochroic dyes. Incident white lightpolarized along one axis is fully transmitted, but is selectivelyabsorbed along the orthogonal axis. For instance, a cyan color polarizerfunctions as a linear polarizer by absorbing the red along one axis. Acolor polarizer that passes a primary color (either additive orsubtractive) along each axis can be formed as a composite consisting oftwo films with crossed axes. Colors are typically selected using crossedcomplementary color (eg. red/cyan) polarizer films coupled with aswitchable polarizer. A full-color device can comprise five polarizingfilms (one neutral), and two switching means. The resulting structuresprovide poor overall peak transmission.

Polarization Interference Filters

The simplest PIFs are essentially two-beam interferometers, where auniaxial material induces a phase shift between orthogonally polarizedfield components. Color is generated by interfering these componentswith an analyzing polarizer. Color switching is accomplished by changingthe phase shift between the arms. The most rudimentary color switchescomprise a single variable retarding means between neutral polarizers.Single stage devices can also incorporate passive bias retarders withvariable birefringence devices. However, these single stage PIFs areincapable of providing saturated color.

PIFs often comprise cascaded filter units in a Lyot structure, eachperforming a distinct filtering operation to achieve improvedselectivity. A polarization analyzer is required between each phaseretarder, reducing transmission. Though adequate color saturation isobtained, multiple-stage birefringent filters are by definitionincapable of functioning as color polarizer. This is quite simplybecause color polarizers must transmit both orthogonal polarizations,which does not permit internal polarizers.

Tuning is accomplished by varying the retardance of active elements ineach stage, maintaining specific relationships between retardances, inorder to shift the pass-band. PIFs use LC elements as variable retardersin order to shift the transmission spectrum. As such, in contrast toSPF, the chromaticity of the active element retardance is not onlyacceptable, it is often an integral aspect of the design. In PIFdesigns, an analyzing polarizer is a static component and tuning isaccomplished by changing the retardance of the filter elements. Whenmultiple active stages are used, the retardances are typically changedin unison to shift the pass-band, while maintaining the basic design.Variable birefringence PIFs can be tuned to provide peak transmission atany wavelength. By contrast, SPFs do not provide tunable color.

Solc filters (Solc (1965), J. Opt. Soc. Am. 55:621) provide high finessespectra using a cascade of identical phase retarders, with completeelimination of internal polarizers. The Solc filter is a specificexample of a much broader class of filters. In this generalization,Harris et al. (Harris et al. (1964), J. Opt. Soc. Am. 54:1267) showedthat any finite impulse response (FIR) filter transmission function canin principle be generated using a stack of properly oriented identicalretardation plates. Numerous researchers have used the network synthesistechnique, along with standard signal processing methods, to generateFIR filter designs. These designs have focussed on high resolution asopposed to broad pass-bands. Tunability, when mentioned, requires thatall retardances are varied in unison.

The color polarizer of the present invention, though using some of thedesign principles of polarization interference filter technology, is acomponent for use in switched-polarizer-filter structures. Prior art PIFdevices require fully active retarder stacks to effectively shift thedesign wavelength of the filter while maintaining the basic design.Conversely, the color polarizers of the present invention use a passiveretarder stack to generate a particular fixed spectral profile which is,as in SPF, invertible by using effective rotation of the analyzingpolarizer.

SUMMARY OF THE INVENTION

This invention provides a complementary color polarizer using a singleneutral polarizing film followed by a stack of two or more retardationfilms. This technology is termed "polarizer-retarder-stack"(PRS). Theuse of more than one retarder in the retarder stack increases the spanof the filter impulse response and the retarder orientations areselected to control the amplitudes of the impulses. In a preferredembodiment, the color polarizers of this invention produce orthogonallypolarized complementary primary colors (red/cyan, green/magenta, orblue/yellow). In combination with a blocking filter, the color polarizerof this invention produces two orthogonally polarized additive primarycolors. Similarly, when a pleochroic color polarizer follows a PRS, itcan produce two orthogonally polarized additive primaries. In analternative structure, a pleochroic color polarizer is used instead ofthe neutral polarizer, and the color polarizer produces two orthogonallypolarized additive primary colors in combination with one unpolarizedadditive primary to give the appearance of two subtractive primarycolors.

This invention further provides color filters which utilize the colorpolarizers of this invention in combination with a polarizationseparator to separate the orthogonally polarized colors. Thepolarization separator can be passive, such as a polarizing beamsplitter, or active, such as a switchable polarizer. The switchablepolarizer can be a rotatable polarizer or a polarization switch incombination with a fixed polarizer. The polarization switch can employ anematic or a smectic liquid crystal cell. The fixed polarizer can be apleochroic color polarizer, in which case one additive primary istransmitted unpolarized. Two color filters of this invention can becascaded to provide a three color (RGB) filter with an off-state. Incombination with a monochrome display, the color filters of thisinvention provide color displays. In combination with a camera orelectronic receiver array, the color filters of this invention provide acolor camera, digital photography and electronic multispectral imaging.

It is a further object of this invention to provide saturated additiveprimary colors, which are not in general produced using single-retardercolor polarizers of the prior art. The term saturated color refers tocolors which appear monochromatic to the human eye. Design of saturatedcolor polarizers can be accomplished using network synthesis techniques,which work backwards from the desired spectrum via the impulse responseto calculate the appropriate retarder stack designs. By proper selectionof number, orientation, and retardance of each component, colorpolarizer designs are identified that transmit substantially all of oneadditive primary band along one axis, and substantially all of thecomplementary subtractive primary band along the orthogonal axis. Theterm subtractive primary band refers to the inverse of an additiveprimary band.

The color polarizer designs of this invention provide arbitrarily narrowtransition bandwidths not achievable with pleochroic dyes or singleretardation film color polarizers. Furthermore, spectral profilessynthesized using finite-impulse-response (FIR) filter designs, permitmultiple transmission maxima in the pass-band, with control of pass-bandripple, and multiple nulls in the stop-band.

It is yet a further object of this invention to provide complementarycolor polarizers with high light efficiency. This is accomplished usingonly a single high-efficiency polarizing film, followed by near losslesspolymer retarder films. Prior art pleochroic dye complementary colorpolarizers require two polarizing films. In the present invention,transmission maxima can be positioned to coincide with source emissionsin each primary color band by means of a simple retardation adjustment.Alternatively, all-purpose PRS designs can be generated that transmit abroad bandpass spanning the entire primary band.

It is still a further object of this invention to providehigh-performance color polarizer structures that are simple to produceand can be fabricated using materials that are readily available. First,this is achieved using designs that provide saturated colors whileminimizing the number of films comprising the stack. Second, the colorpolarizers of this invention can utilize available low-cost highperformance materials produced for the flat-panel display industry. Thisincludes high clarity, uniform retardance, large area stretched polymerretardation films. These films are available in arbitrary retardances(up to 2000 nm), giving the flexibility required to produce designstailored to specific sources. Low-loss adhesive layers can be appliedthat allow easy integration of components. Films with three-dimensionalstretching are also available that provide wider viewing angle, withlittle additional cost. This technology further capitalizes on theavailability of high-efficiency, high-contrast, large-area dichroicpolarizer material for visible (400-700) operation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 a diagram of a PRS used as a separator of complementary primarycolors.

FIG. 2 is a diagram showing reciprocal use of a PRS as a combiner ofcomplementary colors, to form white light in a single polarization.

FIG. 3 is a layout of a square-profile equal-ripple PRS using fiveidentical thickness polycarbonate retarders.

FIG. 4 is calculated additive and subtractive primaries generated by aB/Y PRS color polarizer based on the design of FIG. 3. The retarders arepolycarbonate with a retardance of one full-wave at 600 nm.

FIG. 5a is the measured transmission of a B/Y retarder stack betweenparallel polarizers using the design of FIG. 3. The retarders are NittoNRZ polycarbonate films which were cemented together using the standardadhesive layer. Five 600 nm films were used for the stack. The spectrumshows 98% transmission throughout the subtractive primary, with roughly100:1 blocking throughout the blue primary. The transition bandwidth isquite narrow, allowing a high efficiency green output when combined witha red/cyan stage.

FIG. 5b is the measured transmission of the B/Y retarder stack of FIG.5a between crossed polarizers showing high transmission throughout theblue, with strong rejection of green and red.

FIG. 6 is calculated additive primary spectra generated by a R/C PRScolor polarizer based on the designs of (a) Table 1 and (b) Table 2.

FIG. 7 is the measured transmission of the R/C retarder stack of Table2, design 4, using six 643 nm retarders.

FIG. 8, comprising FIGS. 8a-b, shows example spectra illustrating theparameters given in design Tables 3-8.

FIG. 9 is computer model additive and subtractive spectra for an R/C PRSfor design 5 of Table 3.

FIG. 10 is computer model additive and subtractive spectra for a G/M PRSfor design 5 of Table 4.

FIG. 11 is computer model additive and subtractive spectra for a B/Y PRSfor design 2 of Table 5.

FIG. 12, comprising FIGS. 12a-c, shows the layout of (a) a two-stagefinesse-of-four Lyot filter, and of the equivalent split-elementfilters, including, (b) crossed-retarder and, (c) parallel-retarderconfigurations.

FIG. 13, comprising FIGS. 13a-c, is sample spectra for (a) a two-stageLyot filter containing retarders of order m and 2m, and spectra forsplit-element filters with (b) parallel-retarders and (c)crossed-retarder, showing retardances at peak/null wavelengths. Thecenter retarder is taken to be of order n and the split-element retarderof order m.

FIG. 14 is a computer model additive primary spectrum for an R/Csplit-element PRS for design 4 of Table 6.

FIG. 15, comprising FIGS. 15a-b, is measured spectra of the (a)subtractive primary and (b) additive primary for an R/C PRS using thesplit-element of design 4 of Table 6 and polycarbonate retarders. Thepolarizer is Sanritzu LLC2-5518, and the retarder is Nitto NRFpolycarbonate film. The stack was assembled using the adhesives providedon the standard product.

FIG. 16 is computer model additive and subtractive spectra for a G/Msplit-element PRS for design 6 of Table 7.

FIG. 17 is the measured subtractive primary spectrum for a G/M PRS usingthe split-element of design 4 of Table 7 and polycarbonate retarders.The polarizer is Sanritzu LLC2-5518.

FIG. 18 is computer model additive and subtractive spectra for a B/Ysplit-element PRS for design 4 of Table 8.

FIG. 19 is a computer model additive spectrum for a B/Ydouble-split-element PRS using design 9 of Table 8.

FIG. 20 is a measured subtractive primary spectrum for design 9 of Table8 using polycarbonate retarders. The polarizer is Nitto G1225DU.

FIG. 21 is a diagram showing the use of two PRS stacks to separate whitelight into polarized red, green and blue bands.

FIG. 22 is a diagram showing the use of two PRS stacks to combine threepolarized sources to form white light in a single polarization state.

FIG. 23, comprising FIGS. 23a-b, is block diagrams showing the layout of(a) a single-stage two-color PRS filter and (b) a two-stage four-colorPRS filter.

FIG. 24 is an example of a two-color filter using a rotative achromatichalf-wave polarization switch and a split-element PRS.

FIG. 25 is an example of a three-color filter using two rotativeachromatic half-wave polarization switches and two split-elementretarder stacks.

FIG. 26 is a three-color filter using two rotative achromatic half-wavepolarization switches and two square-profile retarder stacks.

FIG. 27, comprising FIGS. 27a-d, is the measured transmission of thefilter of FIG. 26 in the (a) blue, (b) red, (c) green and (d) off-state.

FIG. 28, comprising FIGS. 28a-d, show the use of PRS color filters insystems including, (a) a single pixel, or imaging receiver, (b) afield-sequential color display using a CRT, (c) a backlit LCDfield-sequential display, and (d) a reflection-mode field-sequentialcolor display illuminated by ambient light.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The color polarizers of this invention, illustrated in FIG. 1, use aneutral linear polarizer 10 in combination with a stack of retarders 20,termed "polarizer-retarder-stack"(PRS). The number of retarders in stack20 and the retardances and orientations of the retarders are selectedsuch that an additive primary spectrum is transmitted along a firstpolarization axis and the complementary subtractive primary spectrum istransmitted along the orthogonal polarization axis. The orientations ofretarders in retarder stack 20 are defined herein with respect to theaxis of polarization of polarizer 10. The retardance of the retarders isspecified herein as the retardance at a design wavelength, typically thepass-band center.

PRS is intrinsically a "complementary color polarizer" technology.Complementary colors are any two colors which, when combined, producewhite. In FIG. 1 the complementary colors are red and cyan (R/C), butthey can alternatively be green and magenta (G/M) or blue and yellow(B/Y). PRS polarizes input white light and then transforms it intoorthogonally polarized complementary colors.

As illustrated in FIG. 1, PRS can be followed by passive polarizationseparator (polarizing beamsplitter) 30 to retain both additive andsubtractive primary bands. This has many applications, particularly inthe field of single-source projection display. Alternatively, PRS can befollowed by an active polarization separator such as a polarizationswitch that effectively modulates the orientation of an analyzingpolarizer to select between the additive or subtractive primary color.Such structures are particularly useful in the field of frame-sequentialcolor video systems, including video cameras and video displays.

PRS can be used in a reciprocal fashion for combining colors, orsuperimposing wavelength bands in a single polarization state, as shownin FIG. 2. A PRS (10 and 20 ) in combination with polarizingbeamsplitter 30 can thus combine orthogonally polarized complementarycolors to produce white light in a single polarization state. Suchstructures are useful for superimposing sources operating in differentwavelength bands, in order to produce colinearly propagating polarizedbeams with no loss of light. Such is the case in projection displaysystems using individual red, green and blue sources.

The present invention teaches a method for designing structures for theeffective isolation of an additive primary color (red, green, or blue)from it's complementary subtractive primary color (cyan, magenta, oryellow). PRS thus provides orthogonally polarized additive andsubtractive primary colors from input unpolarized white light. Prior artpleochroic color polarizers require two polarizing films to accomplishthe same function and consequently have lower throughput. Since asubtractive primary bandwidth exceeds that of an additive primary,nominally by a factor of two, the color polarizer of this invention mustbe more selective than is possible with single-retarder prior artdevices. PRS optimally provides high peak transmission throughout theadditive primary band along one axis, with no transmission of thesubtractive primary band. The complementary spectrum, along theorthogonal axis, provides effective blocking of the additive primaryband and efficient transmission of the subtractive primary band. In apreferred embodiment, this represents multiple pass-band maxima andstop-band nulls, along with a narrow transition bandwidth. This isaccomplished by using additional retarders to increase the content ofthe impulse response and thereby more closely approximate the idealtransmission profile.

Due to the availability of high efficiency neutral polarizer materials,as well as near lossless stretched polymer films, PRS color polarizersare constructed with very high throughput. In addition, the spectraltransmission functions are not constrained by the characteristics ofavailable pleochroic dye materials. This can further enhance throughputby allowing the peak transmission to be tailored to the spectralcharacteristics of the source. Finally, the color contrast and narrowtransition bandwidths provided by PRS designs of this invention providefar superior saturation to that possible with pleochroic dye or singleretarder color polarizers.

PRS Design Optimization

The PRS designs of this invention are produced using several designsteps, including identification of the ideal spectral profile, seriesapproximation of the profile, apodization of the profile, generation ofthe stack design from the profile, and design of the final colorpolarizer at each primary using the profile and real materialparameters. The ultimate stack design results from a fundamentalcompromise between the complexity of the stack (number of retarders andalignment tolerances), and the quality of the transmission spectrum,characterized by saturation and throughput. That is, given an unlimitednumber of impulses and span of the impulse train, the ideal transmissionfunction can in principle be generated. Conversely, the simpleststructure is a single retarder, which generates unsaturated colors thatare inadequate for most purposes. Between these extremes are compromisesolutions that yield very high performance in only a few layers.

In general, a sequence of N retarders generates a total of 2^(N) timeimpulses. When equal thickness retarders are used, this number isreduced to (N+1). Note that when the design allows multiple retarders ofthe same orientation, the retarders can be replaced by a single retarderwith the summed retardance. In a more general sense, zero-orderretardances can be added to any of the elements to producequasi-achromatic retardance shifts. This permits complex impulseresponses, which produce additional design options. The presentinvention comprises structures generating three or more time impulses,with amplitudes selected to optimize color saturation and throughput.These amplitudes are controlled by the orientations and retardances ofthe waveplates and the analyzing polarizer. These parameters aredetermined using the network synthesis method, based on a suitabletruncation of the series describing the optimum profile.

The design begins by specifying the ideal amplitude or intensitytransmission profile for the color polarizer, which accounts for coupledadditive and inverse subtractive spectra. The Fourier transform of thisfunction represents the infinite impulse response. The filter isconstructed using N retarders, representing (N+1) samples of the impulseresponse. Consequently, the spectrum is periodic with period determinedby the separation of time samples, determined by the retardance of eachelement. Since the additive spectrum can have only a single pass-band,this sampling must be sufficiently frequent to insure that higher/lowerorders do not lie in the visible spectrum. This is equivalent to statingthat the order of the retarders determines the free-spectral-range (FSR)of the filter. In practice, the "duty-ratio"(on-state:off-state) of thespectrum depends a great deal on the center wavelength of the particularprimary band, since the rate of retardance change depends strongly oncenter wavelength. Since optimization focusses on minimizing the numberof extraneous time samples, minimizing the FSR required for adequatevisible blocking is the first step. At the minimum FSR, an adjacentorder of the additive primary band lies proximate to, but not inside,the visible range. Although adjacent orders fall outside the visiblerange, a bandtail of an adjacent order may extend into the visiblerange, and ripples can occur in the visible range.

Once the minimum sampling interval is specified, it remains to determinethe number and amplitudes of the impulses. These can simply be theFourier coefficients of the series, truncated at a maximum number.However, truncating with a rectangular window function producespass-band ripple and stop-band side-lobes which degrade performance. Analternative is to first multiply the impulse response function by asuitably tapered window function. Many of these are known in signalprocessing, including Hamming, Hanning, Blackman, and Kaiser windows.The result is a windowed (truncated) Fourier series, which is the inputto the network synthesis program. For still more optimum selection ofimpulse response, iterative design procedures can be used, such asfrequency-sampling, or equiripple design approximations. Once theimpulse response is determined, the retarder/polarizer orientations areselected using the network synthesis technique.

The network synthesis technique (see Harris et al. (1964), J. Opt. Soc.Am. 54:1267, Ammann et al. (1966), J. Opt. Soc. Am. 56:1746, and Ammann(1966), J. Opt. Soc. Am. 56:943) is a procedure for determining theorientations of the N retarders, and the exit polarizer, to obtain thedesired amplitudes of the (N+1) impulses. Since PRS structures produce afinite impulse response, the transmission spectra generated by ananalyzing polarizer depend intimately on the amplitudes of thetime-domain impulses and the orientation of the polarizer. Manytransmission functions which may be suitable for use as complementaryprimary color polarizer can be generated. Furthermore, it is well-knownthat the network synthesis technique generates multiple configurationsfor realizing filters with identical spectral profiles. The simplestdesign to fabricate can be selected from this set. It is thus recognizedthat the specific designs given herein are a sub-set of PRS designscapable of separating additive and subtractive primary bands.

Once the orientations have been selected for the optimum profile, thedesign parameters are analyzed with standard Mueller matrix techniques,which include a dispersion fit to specific retarder materials. Theretardances are then selected to provide optimum color saturation ateach primary for specific materials. The criteria for evaluating PRSdesigns is based on considerations of saturation, hue, and throughput.In any PRS design, one must be concerned with how these parametersaffect both additive and subtractive primary spectra, which areintimately coupled. The saturation and hue are evaluated using the CIEchromaticity diagram. The quality of color generated by a particularfilter output can be characterized by calculating a series of overlapintegrals, including the transmission function for a specific filterstate, the power spectrum of the source, and the CIE color matchingfunctions.

The point describing each output color on the 1931 chromaticity diagramis obtained by the calculation ##EQU1## where α is an index giving thestate of the filter (RGB). The terms are calculated by the overlapintegrals

    X(a)-∫P.sub.s (λ)T(λ,α)x(λ)dλ

    Y(α)-∫P.sub.s (λ)T(λ,α)y(λ)dλ

    Z(α)-∫P.sub.s (λ)T(λ,α)z(λ)dλ

where x, y, z are the 1931 CIE color matching functions. P_(s) (λ) isthe power spectrum of the source and T(λ,α) is the transmission functionof the filter in state α.

Saturated primary colors are generated by maximizing the ratio betweensource power transmitted in the desired primary band to that transmittedoutside of the primary band. Since the PRS design is often matched tothe source characteristics, optimization can be quite specific. Ingeneral, one can state that true white sources, such as a 6000 K blackbody, place greater demand on filter performance than distributedsources, such as a CRT phosphor. In fact, the latter can be regarded awhite source which is effectively preconditioned by a passive filter. Itis well-known that passive filters can always be inserted to rejectbands that lie outside of the primary color bands to increasesaturation.

A particular primary color spans a well defined spectral band of thesource. As such, an ideal PRS permits this entire band to pass with noinsertion loss, while producing high optical density for blocking theremaining light. This implies a very steep transition slope, along witha series of distributed high-contrast nulls in the blocking band. IdealPRS structures can in principle be produced, yet often with aprohibitive number of retarder films. A fundamental design complexitycan be estimated by simply considering the Fourier content of thedesired transmission spectrum, which gives the impulse response. Inpractice, acceptable transition slopes and side-lobeamplitudes/locations must be judiciously chosen to optimize saturationwith a limited number of components.

Since saturation and hue are measures of weighted power ratios, they saynothing specific about the absolute transmission of the structure.Because applications for tunable filters often demand low insertionloss, the throughput is therefore a separate point of optimization.Fundamentally these are at odds since maximum power transmission occursfor full transmission of the source, or maximum desaturation. Inreality, one must select the cutoff wavelengths for each primary colorband initially. It is then reasonable to maximize in-band transmissionexclusively, making the requirements for high saturation and highthroughput compatible.

Filter parameters affecting saturation and throughput are brieflydiscussed in the following. Note that the spectra are described in termsof the additive primary, though it is implied that nulls in the additiveprimary spectrum represent peaks for the subtractive spectrum, andvice-versa.

Peak Transmission: This is maximized by using high efficiency polarizer,low-loss retarders, and a design that minimizes polarization relatedlosses in the primary band. For PRS designs, absorption by the polarizeris typically the dominant source of loss. However, methods known in theprior art for bleaching polarizer can be used to trade null contrast forincreased throughput. Practical considerations, such as AR coatings onexposed polarizer surfaces to minimize Fresnel losses also decreaseglare and insertion loss.

Resolution: From a throughput standpoint, the resolution must besufficiently low to sustain peak transmission throughout the primaryband. From a saturation standpoint, the pass-band resolution must besufficient to isolate only the desired primary band. Designs whichproduce sufficiently low resolution, along with steep transition slopes(or multiple peaks in the pass-band), are preferred.

Transition Band Slope: This is defined by the (10%-90%) bandwidthbetween peak transmission of a primary and the first adjacent null.

Null Transmission: Null contrast is fundamentally determined by thepolarizer extinction ratio, but also relies on the proper retardance andalignment of the stack films. It further assumes no significantdepolarization due to scattering. In practice, 100:1 peak/null contrastis readily achievable, which is far in excess of that required toachieve saturated colors.

Number of Nulls and Their Placement: The number of nulls and theirspectral positions depend upon the stack design and on the retardance ofthe components. It is advantageous to strategically place nulls atout-of-band power spectral maxima.

Side-lobe Amplitude: Side-lobe amplitudes depend upon the specific stackdesign and should be minimized. It is advantageous to place side-lobemaxima away from out-of-band power spectral maxima. Techniques forapodizing the transmission function to reduce side-lobe amplitude can beused to increase performance, often without increasing the numberof-retarders.

Blue/Red Leak: This refers to the free-spectral-range (FSR) orperiodicity of the transmission function. Adjacent orders should beplaced outside the visible or away from source emissions to avoiddesaturation of the primary band.

Source Characteristics: The source characteristics and specialperformance requirements are an important aspect of design optimization.This includes the center wavelengths of the primary band emissions, thedistribution of power within the primary band emissions (bandwidth), andsource emission outside of the primary bands. The polarizer material mayhave a wavelength sensitive transmission (dichroic polarizers aretypically less transmissive in the blue) for which the filter design cancompensate if necessary.

PRS Materials

The materials suitable for the neutral polarizing means includestructures that discriminate between polarization based on absorption,such as dichroic polarizers, and those based on polarization shearing,such as birefringent polarizers, pile-of-plate polarizers, cholestericliquid crystal films, or microprisms. The latter are required forimplementing passive structures for separating or combining colors.Either class can be used in active systems incorporating polarizationswitches.

Polarization shearing structures are usually very transmissive, but areoften expensive and bulky. Dichroic polarizer materials are low cost andare available in large area, such as that by Polaroid, Nitto, andSanritzu. These materials vary in neutrality, peak transmission andextinction ratio. Since it is typically advantageous to maximizetransmission throughout the visible, materials with high neutraltransmission and moderate extinction are desirable. As discussed above,excessive color contrast can be traded for increased transmission bybleaching dichroic polarizer materials. Color polarizers can be used incases where a particular primary is to be passed by the stackunpolarized. Patterned polarizers can be used to pixelate the PRS.

Retardation material employed in PRS stacks preferably provides thefollowing: high optical clarity, uniform retardance, range in retardancesufficient for the design requirements (this depends upon range ofinduced birefringence and practical range in thickness), environmentaldurability, and in many cases large area and low cost.

Retarder stacks can be constructed using layers of form-birefringencedevices, liquid crystal polymer films, stretched polymer retardersheets, or crystalline retarders. Currently, form-birefringence devicesare limited to low retardances due to practical considerations. Theseare either etched, holographically recorded, or deposited highresolution periodic structures that do not diffract light, but impart aphase shift between orthogonal states. It is currently difficult toproduce multi-order low loss visible retarders using form birefringence.

Liquid crystal polymer films, particularly UV cross-linkable polymernematic linear retarders, have potential for forming retarder stacks.However, materials that, when polymerized, form glassy retarder filmsare not as yet commercially available. A potentially attractive featureis the ability to produce thin high-order retarders, since the materialcan have very high birefringence. This can permit the fabrication ofmulti-layer stacks on a single substrate with low cost.

The most attractive materials for the relatively low resolutionrequirements of color generation are currently stretched polymer films.These materials are available in arbitrary retardances (0-2,000 nm),using a variety of materials with unique birefringence dispersioncharacteristics. Large sheets can be purchased at a low cost, permittinglarge clear aperture filters. The characteristics of z-stretchedpolymers (Nitto NRZ) permit large view angles with small retardanceshifts. This is attractive for direct-view applications of the PRS.Several polymer materials are useful in producing PRS, including but notlimited to, poly-vinyl alcohol, polycarbonate, mylar, polypropylene,polystyrene, triacetate (tri-butyl-acetate), and polymethylmethacrylate.

Conventional crystalline retarder materials, such as quartz, mica, andcalcite, are well suited to applications requiring higher resolutionthan that feasible with polymer films. They are also useful forapplications requiring low wavefront distortion, and/or high powerhandling requirements. They are more expensive than polymer retardersand do not lend themselves to large area, particularly when lowretardances are required.

An important aspect of PRS stack design is the wavelength dependence ofretardation. Because retardation is inversely proportional towavelength, it's rate of change depends explicitly on wavelength.Furthermore, the retardance of most materials depends implicitly on thedispersion of the birefringence. The rate of change in retardance isgiven by ##EQU2## where Δn is the birefringence. Dispersion of thematerial birefringence accounts for the second term. For most retardermaterials of interest, the slope of the birefringence spectrum is alsonegative, further increasing the rate of retardance change at shorterwavelengths. The result is a more "compressed" spectrum in the blue thanthat in the red. For this reason, optimum designs can vary significantlydepending upon the particular additive primary band.

The materials used in the PRS designs reported herein are modelled usingthe birefringence dispersion relationship by Wu (Wu (1986), Phys. Rev, A33:1270): ##EQU3## where Γ₀ is the zero-order retardance, m is theretarder order, λ₀ is the design wavelength, and λ* is a mean UVresonance, obtained by measurement. This is done by adjusting λ* untiltheory matches the measured spectrum of the retarder material orientedat 45-degrees between polarizers. Using the above two equations, thedispersion of the birefringence is approximated by ##EQU4## whichverifies that the rate of dispersion is in general negative.

The wavelength dependence of retardance has implications for structuresthat are ideally achromatic, such as polarization switches, and forchromatic structures, such as color polarizers. As described previously,the location of the center wavelength has a profound effect on theresulting duty ratio in the visible. A design with a symmetric dutyratio in the frequency domain has a center wavelength dependent dutyratio in the wavelength domain. Such a design will have a larger dutyratio for a B/Y color polarizer and a smaller duty ratio for a R/C colorpolarizer.

Typically, the design wavelength of structures intended to provideachromatic behavior throughout the visible are skewed toward the blue.Rather than use a 550 nm design wavelength (centered in the visible), anexemplary design uses a shorter wavelength, typically 500 nm for an FLCpolarization switch, in order to compensate for the above effects.

There are virtually an unlimited number of PRS color polarizer designs,subject to specific source characteristics, material dispersion, anddesired output spectrum. Again, it is recognized that any FIR filterthat approximates the ideal spectral profile can in principle begenerated using the techniques described herein. A few specific designexamples generated using the network synthesis technique are describedherein. The first example is based on the decomposition of a symmetricsquare profile, yielding multiple pass-band maxima, a narrow transitionbandwidth, and multiple stop-band nulls. The second example is based onthe Solc filter, which is another specific case of a bandpass designusing equal thickness retarders. The third example is the split-elementfilter, an example of a color polarizer with a complex impulse response.

Square Profile PRS

As discussed previously, there are a number of impulse responsefunctions that represent useful PRS color polarizers. Generalrequirements for producing saturated colors are steep transition slopes,low side lobe amplitudes and effective finesse adequate to isolate theadditive primary spectrum (APS) from the subtractive primary spectrum(SPS). An exemplary general-purpose color polarizer design, forinstance, is one based on the Fourier decomposition of a squaretransmission spectrum. Such a design can be realized by forming theFourier series for a square wave, the coefficients of which are theimpulse response amplitudes, and truncation by an appropriate windowfunction. An alternative technique is to use iterative numerical methodsto arrive at the amplitudes of the impulse response function. Forinstance, given a fixed number of retarders, the transition bandwidthcan be adjusted to obtain a specific maximum pass-band and stop-bandripple. An alternative is to fix the transition bandwidth and allow theripple amplitude to be variable.

The specific example of an optimized PRS using six samples of theimpulse response is shown in FIG. 3. This color polarizer comprisespolarizer 10 and retarders 81 through 85. This polarizer was designed toprovide a fixed ripple amplitude, specifically 1% transmission maximumin the stop-band, and less than 1% maximum loss in the pass-band. Thesampling is such that the duty-ratio of the frequency spectrum issymmetric (50:50). Based on the coefficients of this optimization, theorientations of the retarders were generated using the network synthesistechnique. One solution consists of five films with identical thickness,shown in FIG. 3, where two pairs have the same orientation. The stackcan thus be fabricated using either five sheets of identical retarder,or three sheets with two retardances. In the latter case, retarders 82and 83 are replaced by a single retarder having retardance 2Γ andorientation -15°, and retarders 84 and 85 are replaced by a singleretarder having retardance 2Γ and orientation 10°.

The design of FIG. 3 is based on a symmetric profile, for the samefinesse-of-two given by a single retarder, yet excellent colorsaturation is obtained. This is partially because the definition offinesse, the ratio of the FWHM to the FSR, does not adequately taketransition slope into account. It is further due to the nonlineardependence of retardation on wavelength, and the choice of primary bandcenter wavelength. For instance, a design based on the dispersion ofpolycarbonate yields a blue/yellow color polarizer with an effectivefinesse of three. By contrast, the task of generating a red/cyan filterusing the same symmetric profile design is more formidable, since theretardation characteristics serve to reduce, rather than increase theeffective finesse.

The model (calculated) spectrum of FIG. 4 is based on the colorpolarizer of FIG. 3 employing five polycarbonate retarder sheets, eachwith a retardance of one full-wave at 600 nm. FIG. 4 shows thetransmission of the blue additive primary spectrum and of thecomplementary yellow subtractive primary spectrum. A summary of thespectral characteristics is as follows:

Maxima (100%): 417 nm, 440 nm, 468 nm

Nulls (0%): 546 nm, 600 nm, 670 nm

Side Lobe amplitude: <1.0%

FWHM: 103 nm (400 nm-503 nm)

Effective Finesse: 3

As shown in FIG. 4, the additive primary spectrum of a polarizerdesigned using network synthesis analysis of a square wave profile isitself an approximate square wave. Multiple pass-band maxima andstop-band nulls are distinguishing features of an approximate squarewave spectrum. The multiple maxima and minima flatten the pass-band andstop-band profiles. Sharp transition band slopes are also characteristicof an approximate square wave spectrum. In FIG. 4 the band slope isapproximately 45 nm. In the approximate square wave spectra of thisinvention, preferred band slopes are less than 70 nm. For each of theadditive primary colors, filters can be designed by the networksynthesis technique having band slopes less than 50 nm and, in somecases, less than 40 nm.

FIGS. 5a and 5b show the actual measured spectra of the color polarizer,with near perfect agreement with the model of FIG. 4. The stack wasmeasured between parallel and crossed polarizer, showing complementaryadditive (FIG. 5b) and subtractive (FIG. 5a) primaries. The transmissionwas normalized for source characteristics and Fresnel losses, giving thetransmission of the stack alone. The absorption/interferometric loss ofthe films and adhesive layers, along with any polarization interferencelosses is shown to be roughly 2%. These figures verify high peaktransmission throughout the desired band, very low side-lobes, highcontrast, and narrow transition bandwidths.

Red/cyan color polarizers were also designed by the network synthesistechnique. As described above, network synthesis produces more than oneretarder stack design for a given impulse response function. Table 1lists four different retarder stacks, each having five retarders, whichproduce the same transmission spectrum. The additive primary spectrumfor the five retarder stacks is shown in curve (a) of FIG. 6. Table 2lists nine different retarder stacks, each having seven retarders, whichproduce the same transmission spectrum, shown in curve (b) of FIG. 6.Note that the seven retarder stacks have two more samples of the impulseresponse than the five retarder stacks; curve (b) has more pass-bandmaxima and stop-band nulls than curve (a) and has a sharper transitionband slope.

The color polarizer of design 4, Table 2, was constructed for a designwavelength of 643 nm and the additive primary band transmission wasmeasured (FIG. 7). Because retarder 1 is approximately parallel to theinput polarizer, it was omitted from the fabricated device. The measuredtransmission was normalized for source characteristics and Fresnellosses. The measured spectrum (FIG. 7) shows excellent agreement withthe model spectrum (FIG. 6b). Note that the tail of an adjacentpass-band appears at the blue end of the visible spectrum. This can beremoved by increasing the free-spectral-range of the filter.

Solc-Based PRS Color Polarizers

Solc-based devices also utilize multilayer equal thickness retarders. Inthe case of the folded Solc device, only two unique orientations arerequired., while the films of the fan device "wind" from the inputpolarizer orientation to the orthogonal orientation. In automatedsystems, where the films can accurately be applied at any angle withrespect to the polarizer, this should not present a problem.

The Solc PRS examples shown provide periodic sinc function profiles. Thepass-band consists of a single peak, with adjacent orders separated by aseries of side-lobes. The high side-lobe amplitude is due to the abrupttruncation of the series, though other configurations can produceapodized spectra. Based on a fixed sampling rate (or retarderthickness), the width of the pass-band narrows as the span of theimpulse response is increased. In general, the retarder order isselected to achieve the desired free-spectral-range, and the finesse ofthe filter is proportional to the number N of retardation films.

There are two versions of the Solc PRS, based on folded and fan bandpassconfigurations. The PRS structure consists of a single input neutralpolarizer, followed by a series of at least two retardation films. Theorientations of the films are determined based on the Solc designequations. For the folded version, the retarders are multi-orderhalf-wave retarders. In this case, the subtractive primary band emergesparallel to the input polarizer and the additive primary band isorthogonally polarized. The retarder orientations alternate in signaccording to the rocking angle, α=π/4N with respect to the input.

In the case of the fan filter, the retarders are multiple orderfull-wave plates. The retarder orientations form a fan, and aredistributed according to the angles α,3α, 5α, . . . (2N-1)α with respectto the input polarizer. Using this design for a PRS, the additiveprimary band emerges parallel to the input polarizer, and thesubtractive primary is polarized orthogonal to the input.

Provided that the retarder orientations conform exactly to the Solcdesign equations, a theoretical transmission of 100% is insured at thecenter wavelength of the additive primary. Examples of R/C, G/M and B/YPRS structures were modeled for both folded and fan versions.Dispersionless material was assumed to provide a best-case range inretarder order. Summaries of transmission spectra are provided in Tables3, 4 and 5. The parameters in each table are illustrated in therepresentative spectrum of FIG. 8. Although for generality the spectrumof FIG. 8b shows three pass-bands the additive primary spectra of thisinvention have just one pass-band in the visible spectral range.

Solc Red/Cyan

Folded and fan R/C color polarizers using 2-4 retarders were considered,though additional retarders can be employed to increase resolution. Thefan type with full-wave retarders yielded the optimum FSR. The foldedtype with zero-order half-wave retarders has an excessive FSR, requiringadditional retarders for sufficient resolution. The folded type withfirst-order half-wave retarders exhibited blue leak. A summary of fanversions with one-wave of retardance and folded versions with 1.5-wavesof retardance is given in Table 3. FIG. 9 shows an exemplary R/Cconfiguration (design 5), a folded design with three retarders orientedaccording to a 15° rocking angle. The transmission function exhibits lowside lobe levels, and a fairly sharp transition band slope.Consequently, high transmission is maintained throughout the cyanparallel polarizer spectrum. In addition, the slow change in retardancein the red permits a 100 nm FWHM.

Solc Green/Magenta

Several folded and fan versions were found to produce acceptable G/Mspectra. Again, designs with 2-4 retarders were considered. The minimumretardance was 1.5 waves, which was found to provide moderate resolutionwhen four retarders were used. Retardances as large as three waves wereallowed, due to the symmetry of the blocking in the visible. As such,resolution values ranging from 36 nm to over 100 nm were feasible. FIG.10 shows an exemplary G/M color polarizer using design 5 of Table 4. Thedesign features high resolution, and low side-lobe amplitudes.

Solc Blue/Yellow

The summary data of Table 5 shows folded and fan versions with 1.5 and2.0 waves of retardance, again with 2-4 retarders. The model spectrum ofdesign 2 of Table 5 is shown in FIG. 11. Results of this analysisillustrate that bandpass PRS designs, which increase the finesse witheach additional retarder, are more appropriate at longer wavelengths(R/C). This is because the rapid variation of retardance in the blue,relative to the red, results in unacceptably high pass-band resolution.Since the push for higher resolution is in this case for narrowertransition bandwidths, there is a tradeoff in the blue when usingdesigns that increase finesse in an attempt to better saturation. Thatis, narrow transition bandwidths decrease the throughput of the additiveprimary (and hence desaturate the subtractive primary), while broadtransition bandwidths do not adequately isolate blue and green bands. Asshown in the square-profile example, this problem is solved by usingdesigns that produce narrow transition bandwidths while maintaining lowfinesse.

Split-Element PRS

The split-element filter is a design example based on complex impulseresponse functions, i.e. it includes achromatic as well as chromaticretarders. Split-element filters are described in detail in U.S.application Ser. No. 08/275,006, filed Jul. 12, 1994, which isincorporated herein by reference in its entirety. In split-elementfilters, achromatic retardance shifts are required in the split-elementand center elements to generate the spectrum of a two-stage Lyot filter.Designs allowing complex impulse responses represent additional designoptions in the color polarizers of the present invention. However, sincethey typically require the addition of a zero-order retardance to eachelement, several retardation values can be required to implement thePRS. This is contrasted with designs based on real impulse responses,where equal thickness retarders can be employed. The basic designconsiderations for split-element PRS color polarizer are presented inthe following, along with specific considerations for each primary.

The general design of a split-element PRS color polarizer begins withit's analogy to a two-stage Lyot PIF. The two stage Lyot filter (FIG.12a). The two stage Lyot filter requires three parallel neutralpolarizers 40, 41 and 42, bounding retarder plates 50 and 60. Theretarders have a 2:1 thickness ratio and are oriented at π/4. While aLyot structure cannot function as a color polarizer (due to therequirement for two stages), it does provide bandpass spectra similar tothe split-element filter and is an instructive starting point. As shownin FIGS. 12b-c, the split-element filter is constructed by splitting thethicker element (60) of the Lyot filter and placing the halves (61 and62) on either side of the center retarder (51 or 52), with eithercrossed (FIG. 12b) or parallel (FIG. 12c) optic axes. The centralretarder is oriented parallel or perpendicular to the axis of inputpolarizer 10. The intermediate polarizer of the Lyot filter iseliminated. For a bandpass output, exit polarizer 35 is in generalcrossed with the input polarizer. Note that pure (achromatic) π/2retardances must be added to split-elements 61 and 62 in order toachieve the exact Lyot spectrum. Similarly, for the case of crossedsplit elements, an achromatic π retardance must be added to centerretarder 51. This is not required for center retarder 52 of the parallelretarder device.

FIG. 13a shows the spectrum produced by a Lyot filter, where theretardances are represented by order m and 2m, respectively, at thedesign wavelength. The transmission spectrum is given by

    T(λ)-cos.sup.2 (Γ/2) cos.sup.2 (Γ)

where Γ is the wavelength dependent retardance of the low-order retarder##EQU5## Δn is the dispersive birefringence of the retarder material,and λ₀ is the design wavelength. Because parallel polarizer stagesproduce cosine-squared spectra, peak/null wavelengths of the Lyot filterare identically aligned. That is, both waveplates are full-waveretarders at the peak transmission wavelengths, and the half-waveretardance of the low-order stage coincides with the full-waveretardance of the high-order stage in the blocking band. This producesequal-amplitude side lobes as shown in FIG. 13a.

The split-element PRS comprises polarizer 10 and retarder stack 20 ofFIGS. 12b-c. The retarder stacks comprise either retarders 61, 51 and62a, or retarders 61, 52 and 62b. In the split-element color polarizersof this invention, the subtractive primary spectrum is transmitted alongthe axis of input polarizer 10, and the additive primary band istransmitted along the orthogonal axis. Like a Lyot filter, thesplit-element PRS produces a periodic sinc-squared transmissionfunction, with each peak separated by three nulls. This represents theadditive primary color spectrum. For the inverse spectrum this implies amaximum of three wavelengths with unity transmission to span thesubtractive primary band. Ability to maintain high peak transmission ofthe additive primary color band determines the degree with which it isblocked in the subtractive color spectrum.

There are two design options for the split-element PRS color polarizer:crossed split-elements and parallel split-elements, as shown in FIGS.12b and 12c. Take the sum of split-element retardance to be Γ_(SE), andthe center element retardance to be Γ_(c). In the crossed-retarderconfiguration, the transmission function along the x-axis is given by

    T(λ)-sin.sup.2 (Γ.sub.SE /2)sin.sup.2 (Γ.sub.c /2)

showing mathematically that achromatic half-wave retardances(quarter-wave for each split-element) are required to identicallyproduce a Lyot spectrum. The parallel split-element transmissionfunction

    T(λ)-sin.sup.2 (Γ.sub.SE /2)cos.sup.2 (Γ.sub.c /2)

requires a half-wave shift in the split-element retardance. Thus, thesplit-element retarder is in general a half-wave plate of order m at thewavelength of peak transmission, as shown in FIGS. 13b and c. FIG. 13illustrates the convention for labeling pass-band orders. The centralretarder of order n is either a half-wave plate or a full-wave plate atthe design wavelength, depending upon whether the split-elements arecrossed or parallel, respectively. Because the center element retardancediffers for parallel and crossed split elements, the transmissionspectra produced by each are unique.

When building the color polarizer, it is neither practical nor necessaryto add achromatic quarter-wave or half-wave retardances to the elements.Fortunately adequate color saturation is achieved by simply addingzero-order retardances to the split-elements and the central elementwhen necessary. The use of zero-order retardances precludessimultaneously achieving ideal efficiency of the transmitted wavelength,along with balanced side-lobe levels. In practice, small adjustments inretardance are added to strike a balance between saturation andthroughput. Ignoring this for the moment, the split-element PRS spectraare very nearly the Lyot-like spectra shown in FIGS. 13b and c.

In the PRS color polarizers of this invention, the sum of split-elementretardance is, within a zero-order retardance, in a 2:1 ratio with thecenter element retardance. This allows nearly equal thickness retardersto be used for each element of the stack. Like a Lyot filter, thesplit-element determines the resolution of the filter, while the thinner(central) element determines the spectral period, or free-spectral-range(FSR). For the color polarizers of this invention, the absolutedifference in retardance between each split-element retarder and thecenter retarder at the design wavelength is a quarter-wave, or

    |Γ.sub.SE /2-Γ.sub.c |-1/4WAVES.

This shows that the resolution of the split-element color polarizer iscoupled with the blocking bandwidth.

The lower limit on retardance is that for which the center elementperforms no significant filtering operation. Center element retardancesas low as zero-order half-wave-can provide useful color polarizers,particularly for dispersive materials. The maximum resolution of thecolor polarizer is reached when the FSR is no longer adequate to provideeffective discrimination between primary colors. A ceiling on the centerretarder order can thus be determined, based on "best-case", ordispersionless materials. This ceiling is presented in Tables 6-8summarizing split-element color polarizer designs centered at eachprimary.

In either design, the split-element retardance is m^(th) order half-waveat the transmission peak. For parallel split-elements, the centralretarder is an n^(th) order full-wave retarder, and for crossedsplit-elements it is an n^(th) order half-wave retarder. In general, thesplit-element stage produces adjacent maxima at retardances of (m+3/2)and (m-1/2) waves, which nearly coincide with nulls produced by thecentral stage. For parallel split elements, this occurs for retardancesof (n+1/2) and (n-1/2) waves, respectively. For crossed split-elements,this occurs for retardances of (n+1) and n waves, respectively. The twoadditional nulls between each peak correspond to full-wave retardancesof the split-element, (m+1), m, (m+1), (m+2).

The chromaticity of the required zero-order retardances can create acompromise between peak transmission of the primary, and uniformity ofthe blocking (balance of side-lobe amplitude). This is best shown byexamining FIGS. 13b and c. FIG. 13 shows the maxima and nulls for theideal split-element retarder having achromatic retarders added to thesplit-element retarder and, in FIG. 13c, to the center retarder. Whenzero-order retarders are used instead of achromatic retarders, relativepositions of the maxima and nulls are shifted. For crossedsplit-elements, neither (m+3/2) and (n+1) nor (m-1/2) and n waves ofretardance can occur at the identical wavelength when (m+1/2) and(n+1/2) waves of retardance do, and vice-versa. For parallelsplit-elements neither (m+3/2) and (n+1/2) nor (m-1/2) and (n-1/2) wavesof retardance can occur at the identical wavelength when (m+1/2) and nwaves of retardance do, and vice-versa.

In these filters, the ratio of side-lobe amplitude depends only upon thesign of residual retardance between center and split-elements. That is,when

    (Γ.sub.SE /2-Γ.sub.c)=-1/4T.sub.1 >T.sub.2

and when,

    (Γ.sub.SE /2-Γ.sub.c)-+1/4T.sub.1 <T.sub.2

where T₁ and T₂ are the amplitudes of the side lobes as shown in FIG. 8.In general, symmetric side lobes have the same amplitude, or T₁ =T₁ andT₂ =T₂. The desired relative side-lobe amplitude depends upon thespectral position of nulls relative to the source primary bands. Nullwavelengths depend upon resolution, and the birefringence dispersion ofthe material.

When necessary, there are two methods to compensate for the chromaticityof the zero-order retardances in order to improve side-lobe balance. Onemethod is to shift the relative design wavelengths of center andsplit-elements, which is equivalent to shifting the relativeretardances. This is most appropriate when there is an asymmetricblocking requirement (blue or red, as opposed to green). The secondmethod is to use materials with dissimilar birefringence dispersion tocompensate for the difference in retardance. For instance, when theresidual retardance is negative, a more dispersive material should beused for the split-elements. When the residual retardance is positive, amore dispersive material should be used for the center retarder.

It should be mentioned that the imbalance of side lobe amplitude can bebeneficial in many instances. In some designs, it is actually desirableto further imbalance the side-lobe amplitudes to achieve blockingcharacteristics more suited to the source spectrum. Such cases aredescribed further with respect to specific color polarizer designs.

The spectra generated by split-element color polarizers are summarizedusing the representative spectra of FIG. 8. In general, the additiveprimary spectrum (APS) is represented by a pass-band with peaktransmission T₀ at center wavelength λ₀ and resolution FWHM=(λ_(R)-λ_(B)). By contrast, the subtractive primary spectrum (SPS), theinverse, is represented by a notch. The relative broad bands of hightransmission adjacent to the notch coincide with the complementarysubtractive primary color.

Adjacent to the central pass-band are higher and lower orders that mustbe positioned outside the visible (or away from visible sourceemissions) to avoid blue/red leak, respectively. Transmission of lightby these orders desaturates the APS. Conversely, in the interest ofsimplifying the stack design, the span between the orders should be theminimum bandwidth that produces saturated colors.

Depending upon the particular design, each maximum is separated by aseries of nulls and side-lobes. The location of null wavelengths isindicated in FIG. 8. Since the nulls of the APS coincide with the peaksof the SPS, care must be taken to match the source spectrum with thecritical null wavelengths. It is desirable to minimize the amplitude ofthe side-lobes, represented by T₁ (=T₋₁) and T₂ (=T₋₂).

Split-Element Red/Cyan

The R/C split-element color polarizer experiences the greatestimprovement in saturation and throughput over single retarders. Theincrease from one null (single retarder), to as many as three nulls inthe blocking band provides both high red transmission and excellentsaturation. In spite of the relative slow change in retardance in thered, relative to the blue-green, sharp transition slopes are achievableas well as broad blocking in the blue-green, even with dispersivematerials. The selection of retardances depends most importantly on thebirefringence dispersion, the peak transmission wavelength, and thenearest (green) null wavelength. However, the slope of the red-greentransition band is ultimately limited by blue leak from the higherorder.

Tables 6-8 were constructed for dispersionless materials, representingthe upper limit on retardance (no significant blue leak). Table 6 givesnine red/cyan designs, five of which have crossed split-elements. Thecrossed split-element designs can be identified by half-wave centerretardances. Low retardance split-elements have longer center designwavelengths to permit acceptable blocking in the green. High retardancesplit-elements have shorter center design wavelengths to minimize blueleak. To reduce side-lobe amplitude, relative large differences betweencenter element and split-element design wavelengths were used for lowretardance designs. This has the adverse effect of reducing peaktransmission, as shown. As the order is increased, the difference indesign wavelengths can be decreased, giving greater peak transmission.In all cases, some design wavelength difference is used to balance theside lobe amplitudes. For low retardances, as little as one (broadened)null is present, and at the maximum retardance, as many as three nullsare present. Difference in design wavelength for specified center andsplit-element retardances can equivalently be described as a differencein the retardances with a single design wavelength. When adjusting theretardances to tailor side lobes and nulls, the variation in retardanceis generally less than π/4.

FIG. 14 shows the additive primary spectrum for an R/C color polarizerusing design 4 of Table 6. FIG. 15 shows the measured transmission of anactual R/C split-element color polarizer subtractive primary spectrum(FIG. 15a) and additive primary spectrum (FIG. 15b). The stack is asingle split-element design with crossed split-elements, fabricated withNRF retarder film, and Nitto G1225 polarizing film.

Split-Element Green/Magenta

While the best single retarder designs are G/M filters, due to thesymmetric blocking requirement, a significant improvement is stillrealized in using split-element designs. In single retarder schemes,particularly with dispersive materials, increasing the resolution of thegreen band excessively narrows the blue rejected band. This represents adesaturation of the additive primary band, and a throughput loss for thesubtractive band, particularly in the blue. Conversely, increasing theresolution of the split-element green band broadens the bandwidth ofeach of the two primaries comprising the subtractive primary band. Dueto the large blocking bandwidth between maxima of the split-element, alarge range in green resolution is available. The low resolution limitultimately occurs when the split-element provides spectra no better thanthat possible with a single retarder (two or fewer visible nulls). Thehigh resolution limit occurs when the central stage FSR is insufficient,allowing blue-leak. Within these bounds, the range in retarder order, orresolution, depends a great deal on birefringence dispersion.

As many as three wavelength nulls in the blue and three in the red areavailable for isolating green from magenta. In general (even fordispersionless materials), the maximum resolution is that for whichblue-leak by the higher order maximum begins to desaturate the primary.A total of 12 designs are presented in Table 7 using non-dispersivematerials. A design wavelength of λ₀ =545 nm was arbitrarily selected.In all examples, the design wavelengths for split-element and centralstages are identical, giving a theoretical peak transmission of 100%. Anideal neutral polarizer is assumed in order to differentiate the effectof the retarder stack from other potential losses.

Table 7 shows the characteristics of twelve split-element designs. Withdispersionless materials, the low resolution limit appears to be lessthan 2.5 waves of split-element retardance. With this resolution, asingle red null is present, with one (full-wave center retarder), or two(1.5 wave center retarder) blue nulls. The high resolution limit occurswith 6.5 waves of split-element retardance, where the blue order appearsat roughly 420 nm. A total of 5 nulls are present here, and the finalred null would occur below 700 nm for a slightly lower designwavelength. The corresponding range in resolution is 104 nm FWHM for 2.5waves of split-element retardance, and a 38 nm FWHM for 6.5 waves ofsplit-element retardance.

Design 6, modeled in FIG. 16 is an exemplary split-element G/M colorpolarizer. The spectrum has moderate resolution (70 nm FWHM), and wellplaced nulls. Two blue nulls permit effective blocking, a single nullbeing sufficient in the red. The near side-lobe amplitudes are alsofairly low (3.4%).

When dispersive materials are used, significantly different transmissionspectra result. Birefringence dispersion produces an imbalance betweenblocking bandwidth in the blue and red bands. For instance, apolycarbonate PRS using only 1.5 waves of split-element retardance,gives no red nulls, but produces two blue nulls. The low resolutionlimit, where one red null first occurs, corresponds to a split-elementretardance of 2.5 waves. The high resolution limit occurs at roughly 4.5waves, where the blue order appears at 418 nm. The corresponding rangein resolution is 82 nm for 2.5 waves of split-element retardance, to 45nm for 4.5 waves of split-element retardance.

FIG. 17 shows the measured transmission of a G/M color polarizer basedon Design 4 with a parallel analyzing polarizer. The split-element wasfabricated using NRF retardation film and Nitto G1225 polarizer. Notethat the resolution is considerably higher than Design 4 withdispersionless material (FIG. 16).

The throughput of the subtractive spectrum is intimately connected tothe side lobe amplitude of the additive primary spectrum. The relativeamplitude of side lobes depends upon the relative retardance of thesplit-elements and center retarder. When the split-element retardance isless than twice the center retardance, the side lobes directly adjacentthe pass-band are smaller than the remaining two. When the split-elementretardance exceeds twice the center retardance, the side lobes directlyadjacent the pass-band are suppressed relative to the remaining two.This is most likely the attractive design, though the ultimate choice inrelative retardance depends upon the source characteristics.

Split-Element Blue/Yellow

The challenge in fabricating a high quality B/Y split-element colorpolarizer is to obtain a broad blue transmission band while providingsufficient blocking in the green and red. In the case of the R/C colorpolarizer, the steepest transition slope of the pass-band occurs betweenred and green primaries. This gives the desirable result of a broad redtransmission and effective green blocking. Conversely, the B/Y colorpolarizer has it's shallowest transition slope between the blue andgreen bands. Thus, in providing adequate separation of green and blueprimaries, the resolution of the blue band becomes excessive.Consequently, this represents a degradation of the yellow saturation.This situation is much worse for materials with a large birefringencedispersion. Examples will show that this is where the benefits of thedouble-split-element are most felt.

Double-split-element retarder stacks comprise a center retarder, aninner pair of split-element retarders, and an outer pair ofsplit-element retarders. The inner split-element retarders can beparallel or crossed with each other, as can the outer split-elementretarders. In following example both pairs of split-element retardersare crossed.

Eight split-element B/Y designs were considered for dispersionlessmaterial, along with a single double-split-element design, as shown inTable 8. Design 3 produced acceptably low resolution (FWHM=78 nm), lowside lobe amplitude, and a first null at 550 nm. Designs 1 and 2 hadbroad transition bands, but failed to produce a green null. Design 3 hasthe benefit of a slightly lower resolution than Design 4, along with anarrower transition band, but the side lobe amplitude is quite high inthe red. Designs 5-8 were acceptable, but the blue bandwidth becomesincreasingly narrow. Such designs are most appropriate for sourcespectra with rather confined blue power spectra. FIG. 18 shows theadditive and subtractive primary spectra for design 4.

The double-split-element provides compensation for the increase inretardance at shorter wavelengths. The design permits a slowly varyingtransmission function in the blue, to allow a broad blue pass-band, witha narrow blue to green transition band width. The basic approach is toproduce a sharp blue-green transition slope with a notch in the green,rather than a bandpass in the blue. This eliminates the tradeoff betweenblue-green transition slope and excessive blue resolution. As theresolution of the notch is increased, in part due to birefringencedispersion, the blue band is broadened rather than narrowed. In fact,the double-split-element in general contains the notch transmissionfunction produced by a single split-element with crossed split-elements.With a double-split-element, the notch spectrum is further modulated bythe transmission function for a single retarder between crossed orparallel polarizers. This is a low resolution transmission function thattransmits the blue and rejects the red. The result is a broad bluetransmission function and effective green-red blocking.

Design 9 of Table 8 gives outside and inside split-element retardances,along with the central retardance. Note that the split-elements producethe subtractive (magenta) primary spectrum of Design 5 of the G/Msplit-element (see Table 7). The red is then rejected by thetransmission function of a first-order blue half-wave retarder betweencrossed polarizers. The result is a desirable 97 nm FWHM, a 496 nmcutoff wavelength and a first null at 550 nm. FIG. 19 shows thetransmission function for this design using dispersionless material.

FIG. 20 shows the measured subtractive primary spectrum of a B/Ydouble-split-element fabricated with a stack of Nitto NRF polycarbonateretardation films on a Sanritzu LLC2-5518SF polarizer. The spectrumshows less green transmission than red, due to the characteristics ofthe polarizer. Fresnel losses due to front and back surfaces arepresent, indicating a potential of 89% transmission in the red. The bluetransmission is quite low as can be seen in the figure. A decrease inthe bandwidth of the blue notch is due to the dispersion of theretardation film.

Systems Utilizing PRS

Passive Color Separators and Combiners

When PRS is formed with polarization splitters, reciprocal colorseparators and combiners are formed. FIG. 21 shows a three-colorseparator using two PRS stacks, 20 and 21, neutral polarizer 10, and twopolarization splitters, 30 and 31. White light is converted intopolarized additive primary color bands using B/Y and R/C stacks.Similarly, sources 70, 71 and 72 emitting light at each of the additiveprimaries can be combined into a single white linear polarization stateusing the setup of FIG. 22.

Two-Color Shutters

Since PRS is complementary, it is well suited to providing modulationbetween R/C, G/M or B/Y. Color shutters are formed by combining a PRSstructure with an active polarization separator such as a switchablepolarizer, which can be a polarization switch preceding a staticanalyzing polarizer. A block diagram of a two-color switch is shown inFIG. 23a. The color polarizer comprises neutral polarizer 10 andretarder stack 20. The polarization separator comprises polarizationswitch 90 and analyzing polarizer 15.

The switchable polarizer for use with PRS ideally provides the functionof a neutral polarizer that can be modulated between 0° and 90°orientations. A guest-host dichroic 45-degree tilt FLC polarizer, or acombination of two polarizer-on-demand structures would provide thisfunction. Alternatively, any polarization switching element preceding aneutral polarizer is effectively a switchable polarizer. In general, apreferred switch is one that achieves a half-wave modulation with azero-order retardance (approximately achromatic), low voltage and powerconsumption, a large field of view, low insertion loss, millisecond tosub-millisecond switching, and scaling to large aperture at low cost.

Nematic liquid crystal switching means include homogeneous, π-cell andtwisted and super-twisted device alignments. Compound elements toimprove switching performance, such as the push-pull cell, are alsosuitable. Smectic liquid crystal switches can be made of SmA*(paraelectric), SmC*, distorted helix ferroelectric, antiferroelectric,and achiral ferroelectric devices. The SmA* and SmC* can behomogeneously aligned or surface stabilized. An exemplary ferroelectricliquid crystal switching means is a homogeneous aligned 22.5-degree tiltSmC* half-wave device which switches in orientation between 0 and π/4.Switches are not limited to LC materials, and may include trueelectrooptic effect devices, piezoelectric, or electromechanicalswitches. They can be retarders which reflect the polarization orpolarization rotators.

A drawback of a zero-order half-wave switch is it's inability, due tochromaticity, to provide efficient switching throughout the visible(400-700 nm). Compound elements which provide more achromaticpolarization switching, particularly those requiring only one activedevice, greatly improve performance. A combination of two low-tiltferroelectric liquid crystal (FLC) switches provides enhancedmodulation, and also produces more achromatic polarization switching. Anachromatic rotator is formed in the configuration where, with one fieldpolarity, the optic axes of the cells are crossed and, with applicationof a reverse field, the axes tilt in opposing directions. However, twocells are required per stage, increasing cost, complexity, and reducingtransmission.

A more elegant approach is to combine a single active element withpassive retarders to achieve achromatic switching. Such structures canbe formed by combining one or two passive half-wave retardation filmswith an FLC half-wave retarder to produce a compound achromatic switch.An achromatic half-wave polarization switch is described in U.S. patentapplication Ser. No. 08/419,593, filed Apr. 7, 1995, which is herebyincorporated by reference in its entirety. One embodiment of theachromatic half-wave switch is illustrated in FIG. 24. Switch 90comprises FLC half-wave plate 92 having orientation switchable between5π/12 and 8π/12, positioned between passive half-wave plates 93 and 94oriented at π/12. The composite retardance of switch 90 is a half-waveand the composite orientation switches between 0 and π/4. In otherwords, the three elements together appear like a single rotatablehalf-wave plate switchable between 0 and π/4, but with achromaticretardance. Polarization switch 90 in combination with static polarizer15 functions as a switchable polarizer. When the composite orientationis 0, the polarization is not modulated by the switch and x-polarizedlight is transmitted. When the composite orientation is π/4, y-polarizedlight is flipped to x-polarization and is then transmitted. Theachromatic half-wave polarization switch is a symmetric structure,allowing achromatic switching in both transmission and reflection. Ingeneral, these switches also provide a compensation for spatialvariation in the retardance of the active element that can producevisible color variations.

FIG. 24 shows the layout of a two-color shutter employing FLC compoundachromatic polarization switch 90 with split-element stack 20. Thesplit-element stack comprises center retarder 51 and split-elementretarders 61 and 62a.

The two-color switches described above switch between an additiveprimary and the complementary subtractive primary. Modified devices canswitch between two additive primaries or between two subtractiveprimaries. To switch between two additive primaries, the color polarizeris combined with a passive filter that blocks one of the two additiveprimaries which comprise the subtractive primary output. This blockingcan be achieved using any passive filter, such as dye-type, multi-layerstack, or even PIF optical filters. An appropriately oriented pleochroiccolor polarizer, positioned after the input polarizer, can function asthe blocking filter. The blocking filter can be positioned before,after, or within the active switch. Table 9 lists combinations of activefilters and blocking filters which provide outputs of two additiveprimaries.

To provide two subtractive primaries, the additive primary which iscommon to the two subtractive primaries is left unpolarized orunanalyzed. To achieve this, polarizer 10 and/or polarizer 15 in theswitch of FIG. 23 is a pleochroic color polarizer instead of a neutralpolarizer. A pleochroic polarizer functions as a polarizer only in aspecific wavelength band. For instance, a blue color polarizer polarizesred and green light but leaves blue unpolarized. Any color polarizerwith this characteristic can be employed. When the pleochroic polarizeris positioned at 10, the common additive primary is not polarized at theinput. It therefore is not affected by the retarder stack or polarizerswitch, and is transmitted in both switching states. When the pleochroicpolarizer is positioned at 15, blue light is polarized at the input andis manipulated by the retarder stack and the polarization switch, but itis nevertheless transmitted in both switching states because it is notanalyzed by the exit polarizer. Both polarizers 10 and 15 can bepleochroic color polarizers, allowing the common additive primary topass through unpolarized. The stack must be designed so that itorthogonally polarizes the remaining two additive primaries. There aretwo options for each stack, based on two complementary color polarizers,as listed in Table 10. To provide a cyan/magenta shutter, for example,the common additive primary is blue so the pleochroic color polarizer isblue. The remaining two additive primaries are red and green, which canbe orthogonally polarized by either a red/cyan stack or a green/magentastack.

Full-Color Shutters

When two PRS color shutters are cascaded, full-color switching can berealized. FIG. 23b shows the block-diagram of a two-stage structure thatprovides four output bands, three of which are the additive primarycolors (RGB) and the fourth is an off-state. The full color shuttercomprises a first color polarizer (10 and 20) with a first switchablepolarizer (90 and 15), cascaded with a second color polarizer (11 and21) and a second switchable polarizer (91 and 15). Note that thedirection of propagation through a particular stage is of noconsequence. Therefore, either stage can be swapped end-for-end with nochange in the transmitted spectra, e.g., elements 90 and 20 can beswapped.

Any combination of R/C, G/M, and B/Y PRS color polarizers can be used togenerate the three primary colors. Two primary colors are generateddirectly as the additive primary of the color polarizer, thoughadditional saturation is obtained via blocking by the alternate stage.The third color is generated as the product of the two subtractiveprimary spectra. The fourth color, the off-state, represents the productof the two additive color spectra. Due to the excellent color contrastof the PRS, the fourth state can be a high-contrast off-state. This isoptimally achieved using the two most broadly separated additiveprimaries, red and blue, to insure no overlap of the transition bands.Red and blue primaries are provided by R/C and B/Y PRS structures,respectively. Furthermore, the contrast of the off-state is optimizedfor active units that modulate or effectively modulate the polarizer by90-degrees.

In a preferred embodiment, achromatic compound polarization switches areemployed. In addition to improved color saturation, the highest opticaldensity off-state is obtained with the use of achromatic polarizationswitches. FIG. 25 is an embodiment of the two-stage shutter utilizingachromatic polarization switches 90 and 91. The filter has a B/Y doublesplit-element color polarizer in one stage and an R/C singlesplit-element color polarizer in the other stage.

A two-stage color shutter designed by network synthesis usingsquare-wave profiles is shown in FIG. 26. Retarders are represented asboxes with the retardance and design wavelength listed at the top andthe orientations listed at the bottom. In the case of FLC polarizerswhich rotate between two orientations, the orientations are separated bya comma. Retarder stacks 20 and 21 have B/Y and R/C colors,respectively, and are based on network synthesis square profile designs.The individual color polarizer spectra were shown in FIGS. 5 and 7,respectively. The stacks were constructed with ditto NRZ polycarbonateretarders having a 600 nm design wavelength for the B/Y stack and a 643nm design wavelength for the R/C stack. Polarizers 10, 15 and 11 areNitto G1225 DU polarizers with AR coatings. Polarization switches 90 and91 were fabricated with 500 nm half-wave FLC cells in combination withNitto NRF 500 nm half-wave retardation film.

Experimentally measured output spectra for the design of FIG. 26 areshown in FIG. 27 for the (a) blue, (b) red and (c) green additiveprimaries. The off-state is shown in FIG. 27d. Saturation and throughputare excellent for all three primaries. Losses are attributed almostexclusively to polarizers 10, 15 and 11. These spectra were measuredwith polarized input light; for unpolarized input light the transmissionis halved. After dividing transmission by two, the peak transmission forthe three primary pass-bands averages about 40%. This is about threetimes better than the commercially available full-color shutters.

Color Displays and Cameras

The color switching filters can be combined in various configurations toproduce video cameras or video displays to produce color video systems.Such systems have the advantage that color operation can be achievedwith cameras or displays that are only black and white. Therefore, theneed for three-beam CRTs with shadow masks and RGB phosphor triads isremoved, as is the need for RGB color dots in video cameras and LCdisplays. The systems of the present invention still present or sense asmany different colors as the more conventional systems. That is, anycolor contained in the area of color space defining the three primarybands of the filter can be generated or sensed, as any of the colors canbe composed of a vector comprising admixtures of the components.

FIG. 28a illustrates a multispectral digital camera utilizing the colorfilter of this invention 100 in combination with a monochrome cameracomprising imaging optics 110 and receiver 120. The imaging optics canbe positioned either before or after the color filter. The filter can beeither a two-color or full-color shutter. The full-color filter can beused to provide a field sequential full-color camera.

Color display systems are illustrated in FIGS. 28b-d. They comprisefilter 100 in combination with a monochrome display. The monochromedisplay can be an emissive display or a modulator display. The emissivedisplay (130 in FIG. 28b) can be, for example, a single-electron-beamCRT with a phosphor or phosphor combinations that emit white light.Other examples of emissive displays include active-matrixelectroluminescent (AMEL) displays and field emission devices (FED). Thetransmission-mode modulator display of FIG. 28c utilizes multipixelshutter array 132 in combination with backlight source 131. Thebacklight source can be a lamp or ambient light. The shutter array canhave analog or binary switching and can be, for example, a liquidcrystal display (LCD). High data rate monochrome LCDs can use fastnematic, DHF, or ferroelectric liquid crystal materials, for exampleSmC* or SmA*. The reflection-mode modulator of FIG. 28d uses shutterarray 132 in combination with ambient light and reflector 140. Becausein reflection mode light makes two passive through the color filter,half of a symmetric color filter can be utilized for filter 100. Thereflector can be a digital mirror device 141 which provides a monochromedisplay and eliminates the need for a separate shutter array.

For full color display, field sequential display of the three primarycolors is employed. In order for field-sequential color display systemsto have a pleasing appearance, the primary images must be presented atsufficient rates that the eye fuses them into full-color. Thus,single-display field sequential systems require a minimum frame rate of90 Hz to avoid flicker. Likewise, field-sequential full-color camerasrequire 90 Hz framing to acquire color images at video rates. Fieldsequential displays require an electronic driving means for switchingthe filter through the primary color states in sequence, synchronizedwith the shutter array. Techniques for the design and fabrication ofsuch electronics are well known in the art.

The shutter arrays and the camera receiver are pixelated devices. Thepolarization switches of color filter 100 can also be pixelated. Oneapplication for this is for cases where the camera or display does nothave a response time fast enough to record or display a complete frameat the desired framing speed. In this case the color filter can besegmented such that while one segment is still being recorded ordisplayed, another segment can have moved on to the next color in thesequence. If desired, the passive PRS polarizer itself can be pixelated.

PRS devices can be used in subtractive display systems which usemultiple displays interposed between color and neutral polarizers. Suchsystems produce full-color using a cascade of displays, each operatingon a specific primary band. As such, full-color can be produced usingvideo rate black and white displays.

The PRS color polarizers of this invention have been illustrated withspecific embodiments described above. These embodiments demonstratedesign considerations and the performance of the color polarizers, butare not intended to limit the range and scope of the invention.Sufficient description of structure, design methods and optimizationconsiderations is presented herein to enable one skilled in the art tofabricate virtually endless variations of the color polarizers of thisinvention. Similarly, the color shutters have been demonstrated with buta few of the multitude of polarization switches and liquid crystalpolarization switches known in the art. Application of the color filterof this invention to pixelated displays and recorders has beenillustrated herein. Many more specific embodiments of displays andrecorders, as well as other applications for the color polarizers andcolor filters of this invention will be readily apparent to thoseskilled in the art.

                  TABLE 1    ______________________________________    Five retarder square profile R/C    Retarder     Design #    Orientation  #1     #2         #3   #4    ______________________________________    (1)          66.3   44.1       24.9 11.1    (2)          16.1   10.4       -9.5 12.6    (3)          -23.0  -46.5      21.7 -2.0    (4)          -27.7  -6.7       -37.2                                        -36.7    (5)          -15.4  -33.1      -53.7                                        -72.6    ______________________________________

                  TABLE 2    ______________________________________    Seven retarder square profile R/C    Re-    tarder    Orienta-          Design #    tion  #1     #2     #3   #4   #5   #6   #7   #8   #9    ______________________________________    (1)   -23.0  -4.0   -4.9 -0.8 -23.8                                       -4.1 -5.1 -0.8 -40.9    (2)   57.2   36.4   -47.3                             8.3  56.6 37.2 48.0 8.5  -42.8    (3)   50.7   53.1   -4.2 18.1 52.1 55.8 -2.6 19.3 24.7    (4)   9.3    -13.7  16.8 18.9 12.2 -10.4                                            18.9 21.4 17.0    (5)   -17.1  -18.6  23.1 -3.8 -14.5                                       -16.3                                            26.6 -0.7 -4.5    (6)   -18.2  8.0    -44.1                             -45.4                                  -16.8                                       9.8  -40.9                                                 -43.5                                                      46.1    (7)   -8.3   -45.9  -40.0                             -77.8                                  -7.9 -44.8                                            -39.0                                                 -77.4                                                      -7.0    ______________________________________

                                      TABLE 3    __________________________________________________________________________    Solc R/C               Number         Retardance               of    Design #         (Waves)               Retarders                    Configuration                           FWHM                               λ.sub.3                                  λ.sub.2                                     λ.sub.1                                        λ.sub.B                                           λ.sub.0                                              T.sub.0                                                 T.sub.1                                                   T.sub.2    __________________________________________________________________________    1    1.5   2    FOLDED 121 -- -- 487                                        580                                           650                                              100                                                 --                                                   --    2    1.5   3    FOLDED 102 444                                  488                                     541                                        599                                           650                                              100                                                 1.2                                                   1.2    3    1.5   4    FOLDED  86 428                                  487                                     566                                        610                                           650                                              100                                                 4.3                                                   4.3    4    1.0   2    FAN    125 -- -- 452                                        575                                           680                                              100                                                 --                                                   --    5    1.0   3    FAN    107 -- 447                                     514                                        594                                           670                                              100                                                 1.2                                                   1.2    6    1.0   4    FAN    109 -- 429                                     532                                        592                                           650                                              100                                                 4.2                                                   4.2    __________________________________________________________________________

                                      TABLE 4    __________________________________________________________________________    Solc G/M               Number         Retardance               of    Design #         (Waves)               Retarders                    Configuration                           FWHM                               λ.sub.3                                  λ.sub.2                                     λ.sub.1                                        λ.sub.0                                           λ.sub..1                                              λ.sub..2                                                 λ.sub..3                                                   T.sub.0                                                      T.sub.1                                                        T.sub.2    __________________________________________________________________________    1    1.5   2    FOLDED 135 -- -- 408                                        545                                           -- -- --                                                   100                                                      --                                                        --    2    1.5   3    FOLDED 94  -- 409                                     453                                        545                                           684                                              -- --                                                   100                                                      1.2                                                        --    3    1.5   4    FOLDED 72  -- 408                                     475                                        545                                           640                                              -- --                                                   100                                                      4.3                                                        --    4    2.5   2    FOLDED 80  -- -- 453                                        545                                           680                                              -- --                                                   100                                                      --                                                        --    5    2.5   3    FOLDED 57  426                                  454                                     486                                        545                                           621                                              681                                                 --                                                   100                                                      1.2                                                        1.2    6    2.5   4    FOLDED 43  416                                  454                                     501                                        545                                           598                                              680                                                 --                                                   100                                                      4.3                                                        4.3    7    2.0   2    FAN    100 -- -- 436                                        545                                           700                                              -- --                                                   100                                                      --                                                        --    8    2.0   3    FAN    71  404                                  436                                     473                                        545                                           643                                              -- --                                                   100                                                      1.2                                                        1.2    9    2.0   4    FAN    54  -- 434                                     490                                        545                                           613                                              700                                                 --                                                   100                                                      4.2                                                        4.2    10   3.0   2    FAN    67  -- -- 467                                        545                                           653                                              -- --                                                   100                                                      --                                                        --    11   3.0   3    FAN    47  443                                  467                                     495                                        545                                           607                                              654                                                 --                                                   100                                                      1.2                                                        1.2    12   3.0   4    FAN    36  433                                  465                                     507                                        545                                           589                                              650                                                 --                                                   100                                                      4.2                                                        4.2    __________________________________________________________________________

                                      TABLE 5    __________________________________________________________________________    Solc B/Y               Number         Retardance               of    Design #         (Waves)               Retarders                    Configuration                           FWHM                               λ.sub.0                                  λ.sub.R                                     λ.sub..1                                        λ.sub..2                                           λ.sub..3                                              T.sub.0                                                 T.sub..1                                                   T.sub..2    __________________________________________________________________________    1    1.5   2    FOLDED 90  430                                  440                                     641                                        -- 650                                              100                                                 --                                                   --    2    1.5   3    FOLDED 76  440                                  481                                     552                                        660                                           650                                              100                                                 1.2                                                   1.2    3    1.5   4    FOLDED 59  450                                  482                                     528                                        671                                           650                                              100                                                 --                                                   4.3    4    1.0   4    FAN    89  450                                  499                                     479                                        -- 680                                              100                                                 --                                                   4.2    5    2.0   2    FAN    83  450                                  495                                     598                                        -- 670                                              100                                                 --                                                   --    6    2.0   3    FAN    58  450                                  481                                     531                                        600   100                                                 1.2                                                   1.2    7    2.0   4    FAN    45  450                                  473                                     507                                        594                                           650                                              100                                                 4.2                                                   4.2    __________________________________________________________________________

                                      TABLE 6    __________________________________________________________________________    Split-Element R/C         SE    C         Retardance               Retardance    Design #         (Waves)               (Waves)                     λ.sub.SE                        λ.sub.C                           FWHM                               λ.sub.3                                  λ.sub.2                                     λ.sub.1                                        λ.sub.B                                           λ.sub.0                                              T.sub.0                                                T.sub.1                                                  T.sub.2    __________________________________________________________________________    1    1.5   0.5   650                        756                           131 -- -- 488                                        572                                           662                                              95                                                8.5                                                  --    2    1.5   1.0   680                        630                           117 -- 420                                     510                                        586                                           665                                              96                                                6.4                                                  --    3    2.5   1.0   630                        670                           120 -- 447                                     525                                        582                                           636                                              97                                                6.5                                                  4.5    4    2.5   1.5   650                        630                           107 406                                  473                                     542                                        594                                           645                                              98                                                6.2                                                  14.5    5    3.5   1.5   630                        650                            85 441                                  488                                     551                                        594                                           633                                              98                                                6.9                                                  5.0    6    3.5   2.0   640                        630                            81 448                                  504                                     560                                        600                                           638                                              99                                                6.1                                                  13.2    7    4.5   2.0   610                        620                            63 458                                  496                                     549                                        582                                           612                                              99                                                7.7                                                  4.7    8    4.5   2.5   620                        610                            62 465                                  508                                     558                                        589                                           618                                              99                                                8.1                                                  9.5    9    5.5   2.5   600                        610                            51 472                                  508                                     550                                        578                                           602                                              99                                                6.0                                                  6.8    __________________________________________________________________________

                                      TABLE 7    __________________________________________________________________________    Split-Element G/M         SE    C         Retardance               Retardance    Design #         (Waves)               (Waves)                     FWHM                         λ.sub.3                            λ.sub.2                               λ.sub.1                                  λ.sub.0                                     λ.sub..1                                        λ.sub..2                                           λ.sub..3                                             T.sub.0                                                T.sub.1                                                   T.sub.2    __________________________________________________________________________    1    1.5   0.5   179 -- -- 409                                  545                                     -- -- --                                             100                                                -- --    2    1.5   1.0   159 -- -- 409                                  545                                     -- -- --                                             100                                                -- --    3    2.5   1.0   104 -- -- 454                                  545                                     681                                        -- --                                             100                                                18.9                                                   --    4    2.5   1.5   97  -- 409                               454                                  545                                     681                                        -- --                                             100                                                2.4                                                   --    5    3.5   1.5   73  -- 409                               477                                  545                                     636                                        -- --                                             100                                                14.7                                                   --    6    3.5   2.0   70  -- 436                               477                                  545                                     636                                        -- --                                             100                                                3.4                                                   20.0    7    4.5   2.0   57  409                            436                               490                                  545                                     613                                        -- --                                             100                                                12.7                                                   2.1    8    4.5   2.5   54  409                            454                               490                                  545                                     613                                        681                                           --                                             100                                                4.1                                                   16.7    9    5.5   2.5   46  428                            454                               500                                  545                                     600                                        681                                           --                                             100                                                11.6                                                   2.8    10   5.5   3.0   45  428                            467                               500                                  445                                     600                                        654                                           --                                             100                                                4.5                                                   14.7    11   6.5   3.0   39  443                            467                               488                                  545                                     591                                        654                                           --                                             100                                                10.9                                                   3.3    12   6.5   3.5   38  443                            477                               506                                  545                                     591                                        636                                           --                                             100                                                4.9                                                   13.4    __________________________________________________________________________

                                      TABLE 8    __________________________________________________________________________    Split-Element B/Y         SE    C         Retardance               Retardance    Design #         (Waves)               (Waves)                     λ.sub.SE                        λ.sub.C                           FWHM                               λ.sub.0                                  λ.sub.R                                     λ.sub..1                                        λ.sub..2                                           λ.sub..3                                              T.sub.0                                                 T.sub..1                                                    T.sub..2    __________________________________________________________________________    1    1.5   0.5   430                        410                           110 428                                  510                                     645                                        -- -- 100                                                 -- --    2    1.5   1.0   430                        450                           108 436                                  507                                     645                                        -- -- 99 -- --    3    2.5   1.0   450                        430                           85  447                                  494                                     563                                        -- -- 98 13.5                                                    --    4    2.5   1.5   440                        450                           78  443                                  485                                     550                                        675                                           -- 99 3.7                                                    --    5    3.5   1.5   460                        450                           62  460                                  491                                     537                                        675                                           -- 99 10.8                                                    --    6    3.5   2.0   450                        460                           58  452                                  482                                     525                                        613                                           -- 99 5.9                                                    15.2    7    4.5   2.0   470                        460                           49  469                                  493                                     529                                        613                                           700                                              99 8.0                                                    3.8    8    4.5   2.5   460                        475                           46  464                                  486                                     518                                        594                                           690                                              95 10.5                                                    8.7    9    0.75  1.5   550                        440                           97  447                                  496                                     550                                        660                                           -- 98 4.5                                                    --         1.25    __________________________________________________________________________

                  TABLE 9    ______________________________________    Two Additive Primary Color Shutters                         Blocking                         Filter           Active Filter (Transmitted                                   Output    Design #           (Transmitted Colors)                         Color)    (Transmitted Colors)    ______________________________________    1      Red/Cyan      None      Red/Cyan    2      Red/Cyan      Yellow    Red/Green    3      Red/Cyan      Magenta   Blue/Red    4      Green/Magenta None      Green/Magenta    5      Green/Magenta Yellow    Red/Green    6      Green/Magenta Cyan      Blue/Green    7      Blue/Yellow   None      Blue/Yellow    8      Blue/Yellow   Magenta   Blue/Red    9      Blue/Yellow   Cyan      Blue/Green    ______________________________________

                  TABLE 10    ______________________________________    Two Subtractive Primary Color Shutters                 Dye Type    Output       Color Polarizer                            Stack    ______________________________________    C/M          B          R/C or G/M    C/Y          G          R/C or B/Y    M/Y          R          G/M or B/Y    ______________________________________

We claim:
 1. A method of making a retarder stack for transforming atleast partially polarized light, comprising:selecting a first retarderhaving a first retardance and a first orientation with respect to saidat least partially polarized light for receiving said partiallypolarized light and outputting initially transformed light; selecting asecond retarder having a second retardance and a second orientation withrespect to said at least partially polarized light for receiving saidinitially transformed light and outputting second polarizationtransformed light, wherein said first and second orientations areselected to be different; and arranging said first retarder and saidsecond retarder such that said second polarization transformed lightincludes a first spectrum of output light which is at least partiallypolarized with a first polarization and further includes a secondspectrum of output light which is at least partially polarized with asecond polarization and said first and second polarizations aredifferent, and wherein the retarders are arranged such that theretarders together generate at least three samples of a predeterminedspectral impulse response.
 2. The method of making a retarder stack asclaimed in claim 1, wherein said arranging step comprises arranging saidfirst retarder and said second retarder such that said firstpolarization is orthogonal to said second polarization.
 3. The method ofmaking a retarder stack as claimed in claim 2, wherein said arrangingstep comprises arranging said first retarder and said second retardersuch that said first and second spectra are complements.
 4. The methodof making a retarder stack as claimed in claim 2, wherein said arrangingstep comprises arranging said first retarder and said second retardersuch that said first and second polarizations are linear.
 5. The methodof making a retarder stack as claimed in claim 2, wherein said arrangingstep comprises arranging said first retarder and said second retardersuch that said first and second polarizations are elliptical.
 6. Themethod of making a retarder stack as claimed in claim 2, wherein theorder of said retarders is such that said first spectrum comprises asingle transmission pass-band in the visible spectral range.
 7. Themethod of making a retarder stack as claimed in claim 2, wherein saidfirst polarization and said second polarization are similar andperpendicular.
 8. The method of making a retarder stack as claimed inclaim 2, wherein the order of said retarder is such that said firstspectrum comprises a double transmission pass-band in the visiblespectra range.
 9. A method of making a retarder stack for transformingat least partially polarized light, comprising:selecting and positioninga first retarder to receive the at least partially polarized light, thefirst retarder having a retardance and an orientation with respect tothe at least partially polarized light, wherein the first retarder isadapted to output initially polarization transformed light; selectingand positioning at least one other retarder to receive the initiallypolarization transformed light, the at least one other retarder havingrespective retardances and orientations with respect to the at leastpartially polarized light, wherein the orientations of the retarders aredifferent, and wherein the retarders are adapted to together impart afirst polarization to a first color spectrum of the at least partiallypolarized light, and impart a second polarization to a second colorspectrum of the at least partially polarized light, the first and secondpolarizations being different; and selecting and arranging the number ofretarders, their respective retardances and their respectiveorientations such that the retarders together generate at least threesamples of a predetermined spectral impulse response.
 10. The method ofmaking a retarder stack as claimed in claim 9, wherein the selecting andarranging step comprises selecting and arranging the retarders such thatsaid first polarization is orthogonal to said second polarization. 11.The method of making a retarder stack as claimed in claim 9, wherein theselecting and arranging step comprises selecting and arranging theretarders such that the first and second color spectra are complements.12. The method of making a retarder stack as claimed in claim 9, whereinthe selecting and arranging step comprises selecting and arranging theretarders such that the first and second polarizations are linear. 13.The method of making a retarder stack as claimed in claim 9, wherein theselecting and arranging step comprises selecting and arranging theretarders such that the first and second polarizations are elliptical.14. The method of making a retarder stack as claimed in claim 9, whereinthe number of samples of the spectral impulse generated by the retardersis such that the first color spectrum comprises a single transmissionpass-band in the visible spectral range.
 15. The method of making aretarder stack as claimed in claim 9, wherein the number of samples ofthe spectral impulse response generated by the retarders is such thatsaid first color spectrum comprises a double transmission pass-band inthe visible spectra range.